Multiple interferences comprising multipath fading, permanent narrow-band noise, broadband impulse noise and colored background noises may coexist in a power line channel, which is uncommon for wireless and wired channels. Therefore, information transmission reliability is hard to be guaranteed by applying existing technology of wireless and wired communications directly to power line carrier communication channels, and it is necessary to propose a solution of error-correcting codes with higher reliability to interferences of multiple forms and multiple frequencies in power line carrier communication. Besides, error-correcting codes with higher reliability are still needed for wider wireless transmission environment with interferences of multiple forms and multiple frequencies.
In 2000, Vinck introduced permutation codes into power line carrier communication, and a corresponding dissertation “‘Coded modulation for power line communications’, AEU int. J. Electron. Commun., vol. 54, no. 1, pp: 45-49, 2000” discloses a power line carrier coded modulation method combining permutation code and M-dimension FSK modulation, where time diversity and frequency diversity are introduced simultaneously at a transmitter terminal according to redundancy of permutation codes to increase capability of resisting fading and interferences of multiple frequencies, and a receiving signal is detected by a constant envelope demodulation algorithm at a receiver terminal to form a simple non-coherent demodulation method. It should be noted that Vinck came to a conclusion that permutation codes have an error-correcting capability of d−1 rather than └(d−1)/2┘ through analyzing a permutation code with code length of 4. However, Vinck failed to provide an effective construction method for permutation codes. At present, permutation codes with an error-correcting capability of d−1 develop slowly and are not applied in practice for design methods for algebraic structures of permutation codes are rare and more particularly, the problem of their executable circuits has not been effectively solved yet.